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Detecting stage-wise outliers in hierarchical Bayesian linear models of repeated measures data

  • Outlier Detection
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Abstract

We propose numerical and graphical methods for outlier detection in hierarchical Bayes modeling and analyses of repeated measures regression data from multiple subjects; data from a single subject are generically called a “curve”. The first-stage of our model has curve-specific regression coefficients with possibly autoregressive errors of a prespecified order. The first-stage regression vectors for different curves are linked in a second-stage modeling step, possibly involving additional regression variables. Detection of thestage at which the curve appears to be an outlier and themagnitude and specific component of the violation at that stage is accomplished by embedding the null model into a larger parametric model that can accommodate such unusual observations. We give two examples to illustrate the diagnostics, develop a BUGS program to compute them using MCMC techniques, and examine the sensitivity of the conclusions to the prior modeling assumptions.

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Authors and Affiliations

  1. Department of Statistics, The Ohio State University, 1958 Neil Avenue, 43210-1247, Columbus, OH, USA

    Mario Peruggia & Thomas J. Santner

  2. Biostatistics & Statistical Reporting, Novartis Pharmaceuticals Corporation, One Health Plaza, 07936-1080, East Hanover, NJ, USA

    Yu-Yun Ho

Authors
  1. Mario Peruggia
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  2. Thomas J. Santner
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  3. Yu-Yun Ho
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Peruggia, M., Santner, T.J. & Ho, YY. Detecting stage-wise outliers in hierarchical Bayesian linear models of repeated measures data. Ann Inst Stat Math 56, 415–433 (2004). https://doi.org/10.1007/BF02530534

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  • DOI: https://doi.org/10.1007/BF02530534

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